Question

If x + 1/x =5, find the value of x³+ 1/x³

Answer 1

Given : x + 1/x = 5

 

To find : value of  x³+ 1/x³

 

Solution :  

We have  x + 1/x = 5……..(1)

On cubing eq 1 both sides,  

(x + 1/x)³ = (5)³

By using the identity, (a + b)³ = a³ + b³ + 3ab(a + b)  

x³ + 1/x³ + 3 x × 1/x (x + 1/x) = 125

x³+ 1/x³ + 3 (x +1/x) = 125

x³ + 1/x³ + 3 (5) = 125

x³ + 1/x³ + 15 = 125

x³ - 1/x³  = 125 - 15

x³ - 1/x³ = 110

Hence the value of  x³ - 1/x³  is 110 .

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Answer: 110

Solution:

x + 1/x = 5

For Cubing both the sides, use the identity:

(a + b)³ = a³ + b³ + 3ab(a + b)

So,

(x + 1/x)³ = 5³

x³ + 1/x³ + 3x × 1/x (x + 1/x) = 125

x³ + 1/x³ + 3(x + 1/x) = 125

x³ + 1/x³ + 3 × 5 = 125

x³ + 1/x³ = 125 - 15

x³ + 1/x³ = 110